Ultrahigh Error Threshold for Surface Codes with Biased Noise

Physical Review Letters
David K TuckettSteven T Flammia

Abstract

We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing dominates, is ubiquitous in many quantum architectures. In the limit of pure dephasing noise we find a threshold of 43.7(1)% using a tensor network decoder proposed by Bravyi, Suchara, and Vargo. The threshold remains surprisingly large in the regime of realistic noise bias ratios, for example 28.2(2)% at a bias of 10. The performance is, in fact, at or near the hashing bound for all values of the bias. The modified surface code still uses only weight-4 stabilizers on a square lattice, but merely requires measuring products of Y instead of Z around the faces, as this doubles the number of useful syndrome bits associated with the dominant Z errors. Our results demonstrate that large efficiency gains can be found by appropriately tailoring codes and decoders to realistic noise models, even under the locality constraints of topological codes.

References

Apr 7, 2010·Physical Review Letters·Guillaume Duclos-Cianci, David Poulin
Dec 12, 2012·Physical Review Letters·James R Wootton, Daniel Loss
Dec 3, 2013·Physical Review Letters·Sergey Bravyi, Jeongwan Haah
Jun 14, 2014·Science·D NiggR Blatt
Aug 5, 2017·Physical Review Letters·Giacomo Torlai, Roger G Melko
Sep 10, 2017·Scientific Reports·Stefan Krastanov, Liang Jiang

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Citations

Jun 17, 2018·Physical Review. E·Andrew S Darmawan, David Poulin
Jul 13, 2019·Physical Review Letters·Weilei Zeng, Leonid P Pryadko
Feb 2, 2020·Nature Communications·Jarrod R McCleanHartmut Neven
Aug 28, 2020·Physical Review Letters·Srikrishna OmkarHyunseok Jeong
Apr 18, 2020·Physical Review Letters·David K TuckettBenjamin J Brown
Sep 17, 2020·Science Advances·Shruti PuriS M Girvin
Aug 14, 2020·Nature·A GrimmM H Devoret
Apr 14, 2021·Nature Communications·J Pablo Bonilla AtaidesBenjamin J Brown
Aug 7, 2021·Physical Review Letters·Terry FarrellyThomas M Stace

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